Question

Which equation represents the sequence below?

-10, -8, -6, -4, . . .

(1 point)
Responses

y=−10x+2y is equal to negative 10 x plus 2

y=2x−10y is equal to 2 x minus 10

y=−2x−12y is equal to negative 2 x minus 12

y=2x−12y is equal to 2 x minus 12

Answer 1

To find the equation that represents the sequence \(-10, -8, -6, -4, \ldots\), we first examine the pattern in the sequence:

- The first term is \(-10\).
- The second term is \(-8\) (which is \(-10 + 2\)).
- The third term is \(-6\) (which is \(-8 + 2\)).
- The fourth term is \(-4\) (which is \(-6 + 2\)).

The common difference between consecutive terms is \(2\). This suggests that the sequence is arithmetic with a common difference of \(2\).

The general formula for an arithmetic sequence can be expressed as:
\[
y = mx + b
\]
where \(m\) is the common difference and \(b\) is the first term of the sequence.

In this case:
- The first term (\(y\) when \(x=1\)) is \(-10\).
- The common difference (\(m\)) is \(2\).

We can determine the equation step-by-step:

1. When \(x = 1\), \(y = -10\):
\[
-10 = 2(1) + b \\
-10 = 2 + b \\
b = -12
\]

Thus, the equation is:
\[
y = 2x - 12
\]

So the correct answer from the options given is:
**y = 2x - 12**.